Chromospheric model calculations of the Halpha line for selected red giant branch (RGB) and asymptotic giant branch (AGB) stars in the globular clusters M13, M15, and M92 are constructed to derive mass loss rates. The model spectra are compared to the observations obtained with the Hectochelle on the MMT telescope. These stars show strong Halpha emissions and blue-shifted Halpha cores signaling that mass outflow is present in all stars. Outflow velocities of 3-19 km/s, larger than indicated by Halpha profiles, are needed in the upper chromosphere to achieve good agreement between the model spectra and the observations. The resulting mass loss rates range from 0.6*10^{-9} to 5*10^{-9} Msun/yr, which are about an order of magnitude lower than predicted from Reimers law or inferred from the infrared excess of similar stars. The mass loss rate increases slightly with luminosity and with decreasing effective temperature. Stars in the more metal-rich M13 have higher mass loss rates by a factor of ~2 than in the metal-poor clusters M15 and M92. A fit to the mass loss rates is given by: M [Msun/yr] = 0.092 * L^{0.16} * Teff^{-2.02} * A^{0.37} where A=10^[Fe/H]. Multiple observations of stars revealed one object in M15, K757, in which the mass outflow increased by a factor of 6 between two observations separated by 18 months. Other stars showed changes in mass loss rate by a factor of 1.5 or less.
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